What does 'Enjoy your company' mean?

For starters I am 42 years old and have been divorced for 4 years now I did not start dating until Feb of this year - About a month ago I met a women who is 48 - We get along great - and we compliment one another on a wide variety of different things. When we first met she mentioned she wanted to go slow with things - which is ok with me. We share a kiss now and then and tease a little but nothing sexual has occured in our relationship - Which again is ok with me - But On occassion I see her staring at me and when i ask whats on her mind she doesnt reply - or when I try to mellow the conversation her reply is "Lets just enjoy each others company" I am new to this whole dating thing what exactly does she mean by this? I get a really jacked up feeling when she says that - I almost feel like I am there for convienence - or am I looking at this wrong?

If you feel like she's being vague, then I'd just ask her directly. Taking things slow is fine and dandy, but you deserve to know if your actually going anywhere. Tell her you're developing feelings for her, and just want to see if shes feeling the same. If she can't give you a straight answer, I think that'll be an answer in itself.